A generalization of the Mignotte's scheme over Euclidean domains and applications to secret image sharing

• Main Authors: Ibrahim Ozbek, Fatih Temiz, Irfan Siap
• Format: Article
• Language: English
• Published: Yildiz Technical University 2019-09-01
• Series: Journal of Algebra Combinatorics Discrete Structures and Applications
• Online Access: http://jm.jacodesmath.com/index.php/jacodesmath/article/view/303

Secret sharing scheme is an efficient method to hide secret key or secret image by partitioning it into parts such that some predetermined subsets of partitions can recover the secret but remaining subsets cannot. In 1979, the pioneer construction on this area was given by Shamir and Blakley independently. After these initial studies, Asmuth-Bloom and Mignotte have proposed a different $(k,n)$ threshold modular secret sharing scheme by using the Chinese remainder theorem. In this study, we explore the generalization of Mignotte's scheme to Euclidean domains for which we obtain some promising results. Next, we propose new algorithms to construct threshold secret image sharing schemes by using Mignotte's scheme over polynomial rings. Finally, we compare our proposed scheme to the existing ones and we show that this new method is more efficient and it has higher security.